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A statistician has a series of bivariate data ((6,)), (x212), ... (x,>';)) and wishes to perform a linear regression on these data. State the equation that must be minimised to give the least squares estimates of the regression coefficients. (ii) Derive the least squares estimate of the slope coefficient from the equation in part (1). [5] For a sample of 44 fish, the age (days) and length [ millimetres) of each fish are measured. Denote age by 1" and length by Y. The following summary data are obtained: x; = 3,660, > x7 = 389,684, } y; = 136,727, } y, = 500,813,951, 2X = 13.609.918 (tii) Determine the coefficients for a linear regression of ) on X. [5] (iv) Calculate the sample correlation coefficient between : and v. 121 [Total 13]In the claims department of an insurance office various quantities are computed at the end of each day's business. On Monday, 10 claims are received for a particular class of policy. The mean claim amount is calculated to be f426 and the standard deviation to be f1 12. On Tuesday it is found that one of Monday's claims for $545, was classified wrongly and it is removed from the set of 10 claims. Calculate the resulting mean and standard deviation of the reduced set of 9 claims